Varying refractive index optical medium using at least two materials with thicknesses less than a wavelength

ABSTRACT

An optical medium has a graded effective refractive index with a high maximum refractive index change. The medium is formed using alternating layers of two or more materials having significantly different refractive indices. The thickness of the layers of at least one of the materials is substantially less than the effective light wavelength of interest. The effective index of refraction in a local region within the medium depends on the ratio of the average volumes of the two materials in the local region. A graded index of refraction is provided by varying the relative thicknesses of the two materials.

The present patent document is a divisional application of U.S.application Ser. No. 10/652,269, which claims the benefit of the filingdate under 35 U.S.C. § 119(e) of Provisional U.S. Patent ApplicationSer. No. 60/406,704, filed on Aug. 28, 2002, both of which are herebyincorporated by reference in their entirety.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No.11/216,758, “Integrated Planar Composite Coupling Structures forBi-Directional Light Beam Transformation Between a Small Mode SizeWaveguide and a Large Mode Size Waveguide,” filed Aug. 31, 2005, andissued as U.S. Pat. No. 7,218,809 on May 15, 2007, which is acontinuation of U.S. patent application Ser. No. 10/083,674, filed Oct.19, 2001, and now abandoned, the disclosures of which are herebyincorporated by reference.

This application is also related to U.S. patent application Ser. No.10/651,372, “Optical Beam Transformer Module for Light Coupling betweena Fiber Array and a Photonic Chip and the Method of Making the Same,”filed on Aug. 28, 2003, and issued as U.S. Pat. No. 7,303,339 on Dec. 4,2007, the disclosure of which is hereby incorporated by reference.

This application is also related to pending U.S. patent application Ser.No. 09/884,691, “Method for Forming a Refractive Index Patterned Filmfor Use in Optical Device Manufacturing,” filed Jun. 19, 2001, thedisclosure of which is hereby incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to structures having arefractive index distribution and in particular to an optical mediumhaving an arbitrary desired effective refractive index distributionusing at least two materials with thicknesses less than a wavelength.

Optical communication systems require optical components to guide and/ormanipulate a light beam in continuous or pulse format. Of the variousoptical components used in optical communication systems, some have acontinuous change in the distribution of the refractive index. Examplesinclude graded refractive index multimode optical fibers [e.g., Cohen etal., “Multimode Optical Fiber,” U.S. Pat. No. 3,989,350, Nov. 2, 1976;Fleming, Jr., “Multimode Optical Fiber,” U.S. Pat. No. 4,033,667, Jul.5, 1977 and graded refractive index rod lenses [e.g., Ho Shang Lee,“Miniaturization of Gradient Index Lens Used in Optical Components,”U.S. Pat. No. 6,088,166, Jul. 11, 2000]. A continuous refractive indexchange can serve various purposes, including light beam collimation,focusing, imaging and the like [Duncan T. Moore, “Gradient Index Optics:A Review,” Applied Optics, Vol. 19, No. 7, 1 Apr. 1980].

Traditionally, such graded refractive index (“GRIN”) devices have beencreated by mixing different materials. Most of these methods involve adominant material and another material that is either used as a dopantor dispersed in the dominant material [e.g., Park et al., “ProductionMethod for Objects with Radially-Varying Properties,” U.S. Pat. No.6,267,915 B1, Jul. 31, 2001]. As there is generally a limit to theamount of dopant that can be uniformly distributed inside the dominantmaterial, the maximum refractive index change (Δn) that can be achievedusing such a method is generally less than 0.1. As a result, when such amethod is used to make a graded refractive index lens to focus a lightbeam, the light focusing power of the lens is generally low. In otherwords, the focal length of such a lens is relatively long, and thefocused beam spot size is relatively large (typically a few microns). Atypical example is an ion exchanged glass based GRIN rod lens, such aslenses made by GRINTECH GmbH, for which the focal length (also called aquarter pitch) is on the order of millimeters and the focused beam spotsize is on the order of a few microns.

Various techniques for producing GRIN devices having an essentiallycontinuous refractive index change have been developed. A first methoduses neutron irradiation, in which a boron rich glass is bombarded withneutrons to create a change in the concentration of boron and hence achange in the refractive index of the material [P. Sinai, AppliedOptics, Vol. 10, pp 99 (1971)]. This method has limited applicationbecause the gradient is not permanent, and the maximum index change isonly about 0.02.

A second method uses chemical vapor deposition (CVD) to create a fiberpreform for a GRIN optical fiber. A glass material of a given refractiveindex is deposited on either the inside or outside of a tube. Asuccession of layers having slightly different chemical compositions(e.g., slightly increased or decreased dopant concentrations) is thendeposited. Each layer generates a small step in the refractive index.After the preform, which typically has a diameter of about 2.5 cm, ismade, a fiber is drawn from it. As the fiber is drawn, the layers becomeso thin that the refractive index distribution becomes effectivelycontinuous [e.g., Cohen et al., “Multimode Optical Fiber,” U.S. Pat. No.3,989,350, Nov. 2, 1976; Fleeting, Jr., “Multimode Optical Fiber,” U.S.Pat. No. 4,033,667, Jul. 5, 1977; Dabby et al., “Graded Start Rods forthe Production of Optical Waveguides,” U.S. Pat. No. 4,298,366, Nov. 3,1981; Dabby et al., “Graded Optical Waveguides,” U.S. Pat. No.4,423,925, Jan. 3, 1984]. The maximum index change that can be achievedusing this technique is about 0.01.

A third method involves producing a graded refractive index in organicor plastic materials. For instance, multiple plastic layers ofsuccessively increasing or decreasing refractive index can be depositedon a plastic cylinder or planar surface; the material is then cured[e.g., Toyoda et al., “Distributed Graded Index Type OpticalTransmission Plastic Article and Method of Manufacturing Same, “U.S.Pat. No. 5,390,274, Feb. 14, 1995; Nakamura, “Method and Apparatus forManufacturing Distributed Refractive Index Plastic Optical Fiber,” U.S.Pat. No. 6,132,650, Oct. 17, 2000]. In related processes, monomers canbe changed to polymers or cross linking of polymers can be enabled usingeither thermal radical polymerization (induced by UV or laser light,photodimerization, or electron ray) or condensation polymerization(induced by radical addition or photodimerization) [e.g., Jung et al.,“Manufacturing Method of a Polymer GRIN Lens Using Sulfonation,” U.S.Pat. No. 5,567,363, Oct. 22, 1996]. The disadvantages associated withplastics include the relatively strong absorption of light in thestandard communication wavelength band, as well as the relatively lowthermal and lifetime stability of the plastic material. Althoughattempts to address these problems—e.g., by replacing the C—H bond by aC—F bond [Sugiyama et al., “Graded Refractive Index Optical PlasticMaterial and Method for its Production,” U.S. Pat. No. 6,166,125, Dec.26, 2000]—have been somewhat successful, the optical communicationindustry still generally prefers not to use plastic gradient lenses.

A fourth method, ion exchange, is commonly used to make glass-basedgraded refractive index rod lenses. Ions from a molten salt, e.g.,lithium bromide or potassium nitrate, diffuse into glass and areexchanged with larger ions in the glass [e.g., Senapati et al., “GradedIndex Lens for Fiber Optic Applications and Technique of Fabrication,”U.S. Pat. No. 6,128,926, Oct. 10, 2000; Senapati et al., “Graded IndexLens for Fiber Optic Applications and Technique of Fabrication,” U.S.Pat. No. 6,172,817 B1, Jan. 9, 2001]. The possible refractive indexdistribution is limited by the diffusion process, and the maximumrefractive index change is only about 0.05.

A fifth method is ion or molecular stuffing, in which heat is applied toseparate the phases of a special glass in which one of the phases isdissolvable in an acid. After acid treatment, the glass is immersed in abath to allow other ions or molecules to diffuse into the glass pores;alternatively, the pores may be left behind. The glass is then condensedby heating [e.g., R. K. Mohr et al., Digest of Topical Meeting onGradient-Index Optical Imaging Systems (Optical Society of America,Washington, D.C., 1979), paper WA I; Macedo et al., “Method of ProducingOptical Wave Guide Fibers,” U.S. Pat. No. 3,938,974, Feb. 17, 1976.However, most glasses that are well accepted for optical communicationdo not possess the required uniform phase separation property. Inaddition, the maximum refractive index change is still only about 0.05.

A sixth method involves a “sol-gel” technique, in which a solution ofmultiple metal oxides is spin coated or dip coated on a surface. Heattreatment follows to evaporate the solvent and condense the metaloxides, thereby forming a thin layer of glass film. To create a gradedrefractive index multiple layers having different metal oxide contentcan be successively deposited. One problem with this technique is thatcracking of the film tends to occur as the film grows thicker and theamount of dopant in the solution increases. It is thus difficult toproduce a film thickness of the order of about 10 μm. In an alternativeprocess, a gel glass film or gel glass rod can be made first, and glassphase separation can be induced by heat treatment followed by selectiveleaching or etching to create a microporous structure with a gradedrefractive index [e.g., McCollister et al., “Process of Making GlassArticles Having Antireflective Coatings and Product,” U.S. Pat. No.4,273,826, Jun. 16, 1981; S. P. Mukherjee et al., “Gradient index ARFilm Deposited by the Sol Gel Process,” Applied Optics, Vol. 21, No. 2,p. 283, Jan. 15, 1982; S. Konishi et al., “r-GRIN Glass Rods Prepared Bya Sol Gel Method,” Journal of Non Crystalline Solids, Vol. 100, pp. 511513 (1988); Debsikdar, “Broadband Antireflective Coating Composition andMethod,” U.S. Pat. No. 4,839,879, May 16, 1989]. Again these methods canonly produce a maximum index change of about 0.1.

A seventh method involves UV imprinting of photosensitive glasses todisrupt the metal oxygen bond, thereby inducing a refractive indexchange. This technique is commonly used to make fiber Bragg gratings(FBG), which are common components in today's fiber-optic communicationsystems. The most commonly used material is germanium doped silicafiber. After hydrogen loading and UV laser imprinting, the maximum indexchange is about 0.1. Another glass of higher photosensitivity is leadoxide, but it has been found that the maximum achievable index changefor UV imprinting of lead oxide is only about 0.2 [see theabove-referenced co-pending U.S. patent application Ser. No. 09/884,691.

An eighth method makes use of centrifugal force applied during thecombustion synthesis of composite materials, with the result that thecomposition and particle size of the metallic or ceramic componentchanges continuously across the thickness of the product [e.g., Munir etal., “Centrifugal Synthesis and Processing of Functionally GradedMaterials,” U.S. Pat. No. 6,136,452, Oct. 24, 2003. This method involvesapplying a glass melting high temperature to a rotating mold containingglass powder, mixtures. As in the glass melting methods involvingdopants, there is a maximum concentration of the metallic or ceramiccomponent that can be achieved without clustering. Consequently, themaximum index change that can be achieved is small (about 0.1).

None of these methods is able to produce a maximum index change greaterthan about 0.2. In addition, none of these methods is able to produce anarbitrary refractive index profile with high precision because thesemethods generally rely in some way on diffusion of one material intoanother, which cannot be precisely controlled. In some applications, forinstance, light coupling between a single mode optical fiber and a III-Vcompound semiconductor waveguide, a graded refractive index device witha maximum refractive index change greater than about 0.2 would bedesirable. Such a device would provide higher focusing power and asmaller focused spot size than GRIN devices produced by existingtechniques.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention provide a device having a graded(or distributed or gradient) effective refractive index profile with avery high maximum refractive index change. According to one aspect ofthe present invention a light transmitting device with a graded index ofrefraction includes alternating layers of two (or more) materials havingsignificantly different refractive indices (e.g., a difference of atleast 0.2). The thickness of the layers of at least one of the materialsis substantially less than the effective light wavelength of interest.The effective index of refraction in a local region within the devicedepends on the ratio of the average volumes of the two materials in thelocal region; because the relative thicknesses of the layers can be madedifferent for different layers, a graded index of refraction can beprovided. Control of the layer thicknesses also allows an arbitraryrefractive index profile to be provided.

According to another aspect of the present invention, a lighttransmitting device having a graded index of refraction includes a bodymade substantially of a first material, such as an amorphous material.Embedded in the body area number of discrete structures comprising asecond material (e.g., another amorphous material), each of the discretestructures having a size in at least one dimension substantially smallerthan an effective wavelength of light in the second material. The firstmaterial has a first index of refraction and the second material has asecond index of refraction different from the first index of refraction;in one embodiment, the first and second indices differ by at least 0.5.The size of the discrete structures in the at least one dimension isdifferent in a first local region of the body than in a second localregion of the body, thereby providing a graded index of refraction. Inone embodiment, the discrete structures include substantially planar (orcurved) layers having a size in one dimension that is substantiallysmaller than an effective wavelength of light in the second material. Inanother embodiment, the discrete structures include filamentarystructures having a size in two dimensions that is substantially smallerthan an effective wavelength of light in the second material. In yetanother embodiment, the discrete structures include grains having a sizein three dimensions that is substantially smaller than an effectivewavelength of light in the second material.

According to another aspect of the present invention, a lighttransmitting device having a graded index of refraction includes aplurality of alternating layers of a first material and a secondmaterial, each layer of the second material having a thicknesssubstantially less than an effective wavelength of light in the secondmaterial. The first material has a first index of refraction, and thesecond material has a second index of refraction different from thefirst index of refraction; in one embodiment, the first and secondindices differ by at least 0.5. The plurality of alternating layersforms a light-transmitting medium with an effective index of refractionin a local region that depends on a local ratio of a volume of thelayers of the first material to a volume of the layers of the secondmaterial. A graded effective index of refraction along a directiontransverse to the layers is formed by varying the thicknesses of thelayers. The thickness of each layer of the first material can also bemade to be substantially less than the effective wavelength of light inthe second material. Amorphous materials, such as silicon dioxide andtitanium dioxide, can be used as the first and second materials.Polycrystalline materials can also be used. The layers may be planar orcurved to provide light beam focusing in two dimensions. A variety ofrefractive index distributions, including parabolic distributions, canbe provided. The distribution can also be optimized to provide modematching between other light-transmitting devices (e.g., between asingle mode optical fiber and a III-V semiconductor waveguide).

According to another aspect of the present invention, a lighttransmitting device having a graded index of refraction includes aplurality of alternating layers of a first amorphous material having athickness and a second amorphous material, each layer of the secondmaterial having a thickness substantially less than an effectivewavelength of light in the second material. The first material has afirst index of refraction, and the second material has a second index ofrefraction different from the first index of refraction. The pluralityof alternating layers forms a light-transmitting medium with aneffective index of refraction in a local region that depends on a localratio of a volume of the layers of the first material to a volume of thelayers of the second material. A graded effective index of refractionalong a direction transverse to the layers is formed by varying thethicknesses of the layers. The refractive index profile can becontrolled so as to provide a desired focused optical spot size and mode(wavefront) profile for transmitted light.

According to another aspect of the present invention, an optical moduleincludes a substrate assembly that has a photonic chip mounting regionand a groove extending toward the photonic chip mounting region. Theoptical module also includes an optical coupler having a graded index ofrefraction disposed between the groove and the photonic chip mountingregion. The optical coupler includes a plurality of alternating layersof a first amorphous material and a second amorphous material, eachlayer of the second material having a thickness substantially less thanan effective wavelength of light in the second material. The firstmaterial has a first index of refraction, and the second material has asecond index of refraction different from the first index of refraction.The plurality of alternating layers forms a light transmitting mediumwith an effective index of refraction in a local region that depends ona local ratio of a volume of the layers of the first amorphous materialto a volume of the layers of the second amorphous material. A gradedeffective index of refraction along a direction transverse to the layersis formed by varying the thicknesses of the layers. A photonic chip canbe mounted in the photonic chip mounting region, and an optical fibercan be mounted in the groove.

The following detailed description together with the accompanyingdrawings will provide a better understanding of the nature andadvantages of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of light propagation in a medium with aparabolic refractive index distribution;

FIGS. 2A-B are schematic diagrams representing the use of two materialsto realize a parabolic effective refractive index distribution accordingto the present invention;

FIGS. 2C-D are graphs of the effective index distribution as a functionof position for the structure in FIGS. 2A-B;

FIG. 3 is a graph of transmittance as a function of the normalizedthickness of a thin layer of one optical medium sandwiched in anotheroptical medium;

FIGS. 4A-B are graphs of a computer simulation of light propagationthrough a parabolic refractive index distribution realized with multiplematerials and with two materials, respectively;

FIGS. 5A-B are graphs of simulated light coupling from a GRIN lens intoa mode matched waveguide for a parabolic refractive index distributionrealized with two materials and with multiple materials, respectively;

FIG. 6 is a scanning electron microscope (SEM) image of a GRIN structurerealized by depositing alternating thin layers of two materials ofdifferent layer thickness on a flat silicon substrate;

FIGS. 7A-B are graphs showing the measured focused spot profile andinput spot profile for a one dimensional GRIN lens realized using Si0₂and Ti0₂; and

FIGS. 8A-D are schematic diagrams illustrating process steps forfabricating a GRIN device from curved layers of two materials.

DETAILED DESCRIPTION OF THE INVENTION

As is generally known, light is an electromagnetic wave oscillating athigh frequency. All portions of the electromagnetic spectrum are meantto be included, including but not limited to, radiowaves, microwaves,millimeter waves, infrared radiation, visible light, and ultravioletradiation. When light travels through a dielectric medium (e.g., glass),its speed (v) is reduced relative to the speed of light in vacuum (c).The refractive index (n) of the medium is defined as n=c/v. Thefrequency of the light is unchanged, and the wavelength is reduced fromλ_(o) in vacuum to λ_(eff)=λ_(o)/n in the medium.

As shown in FIG. 1, in a graded refractive index (“GRIN”) optical medium100, the material has a refractive index n(r) that decreasessubstantially continuously from a value of no at the central axis (r=0)to a value of n_(b) at the outside border (r=a). In this example, n(r)has a parabolic refractive index distribution given by the formula:

${{n(r)} = {n_{o}\left\lbrack {1 - {\Delta \left( \frac{r}{a} \right)}^{2}} \right\rbrack}},\mspace{14mu} {{{where}\mspace{14mu} \Delta} = {\frac{n_{0} - n_{b}}{n_{0}}.}}$

This index distribution will cause light rays 110 propagatinglongitudinally through medium 100 to bend towards the central axis andto be periodically refocused. If the optical medium is cut to the rightlength (f), the medium can function as a lens to focus or expand andcollimate a beam of light. The focal length (or quarter pitch) of such aGRIN lens is given approximately by

$f = {\frac{a\; \pi}{2\sqrt{2\; \Delta}}.}$

In general, the focused spot size for any light beam or pulse is finite.The shorter the focal length of the lens, the smaller the focused spotsize. Accordingly, a smaller focused spot size can be achieved byincreasing Δ (which is dominated by the index change between the centralaxis and the outside border), by decreasing α (the distance between thecentral axis and the outside border), or both. At the same time, thereis a physical diffraction limit; consequently, the smallest focused spotsize of any wave will only be about the size of the wavelength in themedium where focusing occurs. In the case of a GRIN lens, the focusedlight beam is located near the central axis, where the refractive indexis the highest. Hence, if a high refractive index material is used atthe central axis, a much smaller diffraction limited beam spot size canbe achieved because the wavelength of light in a material is equal tothe vacuum wavelength divided by the refractive index of the material.If the focused light beam is coupled into another mode matchedwaveguide, a highly efficient light coupling between the GRIN lens andthe waveguide can be achieved, as will be described further below.

In principle, a graded refractive index distribution can be constructedfrom multiple thin layers of optical media with different refractiveindices. If the layer thickness is small enough, there is a negligibledifference in the focusing effect between a continuously gradedrefractive index distribution and a step graded refractive indexdistribution provided by multiple thin layers of materials withdifferent refractive indices. Accordingly, a parabolic refractive indexdistribution can be produced by depositing multiple thin layers ofdifferent materials selected so that the refractive index decreases withdistance from the central axis.

Embodiments of the present invention employ two (or more) materialshaving a relatively large refractive index difference to create astructure having a graded refractive index (e.g., a parabolicdistribution). By using a high refractive index material such as silicon(n=3.4), the refractive index at the central axis of the parabolic GRINstructure can be made quite high, and hence the spot size of the focusedlight beam can be quite small (e.g., less than 0.5 μm for light having awavelength of 1.5 μm in air).

When an optical medium with a dimension that is substantially smallerthan the effective wavelength of light is embedded in another opticalmedium of a different refractive index, the result is an effectiverefractive index with a value between those of the two optical media.FIG. 2 illustrates the principle. A medium 200 provides an approximatelycontinuous parabolic refractive index distribution by using multiplelayers 205 of materials having different refractive index as shown inFIG. 2A. Each layer 205 is constructed from a number of thin layers 212,214 of two materials of different refractive indices, as shown in FIG.2B. Each material's optical thickness is substantially less than theeffective wavelength of light in the material. The effective refractiveindex 215, illustrated in FIGS. 2C-D, is approximately

${n_{eff} = \frac{{n_{1}L_{1}} + {n_{2}L_{2}}}{L_{1} + L_{2}}},$

where n₁ and n₂ are the refractive indexes of the two materialsrespectively, and L₁ and L₂, are the total thickness of the respectivematerials within a local region larger than the effective wavelength ofthe light. This can be generalized to a medium with a mixture of twoparticles with different refractive indices, in which

${n_{eff} = \frac{n_{2}\left\lbrack {{\frac{V_{1}}{V_{2}}\frac{n_{1}}{n_{2}}} + 1} \right\rbrack}{\left\lbrack {\frac{V_{1}}{V_{2}} + 1} \right\rbrack}},$

in which V₁ and V₂ are the volumes of the first and second materials.Other layers in medium 200 are made of the same materials, but withdifferent thicknesses L₁ and L₂, thereby providing different n_(eff).

There are concerns about the effectiveness of using two materials toachieve the effect of a real continuous refractive index distribution.One concern is the light transmission efficiency through the manyoptical interfaces of the structure. A second concern is how effectivelythis structure focuses light. A third concern is the total amount oflight that will be lost when light is focused using this structure.These concerns will now be addressed.

High light transmission efficiency can be provided by using sufficientlythin layers of the two materials. As is generally known in the art andillustrated in FIG. 3, when a light beam shines through a thin film 310of thickness d, having a refractive index n₂, sandwiched in anotheroptical medium 312, the light transmittance (defined as the amount oflight energy transmitted through the film divided by the amount of lightenergy incident onto the film) is given by

${{T(d)} = {\frac{I_{trans}}{I_{inc}} = \frac{\left( {1 - R} \right)^{2}}{\left( {1 - R} \right)^{2} + {4R\; {\sin^{2}\left( {k_{1}d} \right)}}}}},\mspace{14mu} {{{where}\mspace{14mu} k_{1}} = {\frac{2\; \pi}{\lambda_{eff}} = {\frac{2\; \pi \; n_{2}}{\lambda}\cos \; \theta}}},$

with λ being the wavelength of light in vacuum, θ being the angle ofrefraction in the thin film 310, and R being the reflectance of the thinfilm. FIG. 3 shows the transmittance of light as a function of d/λ_(eff)for a light beam traveling from silica (SiO₂, n₁=1.45) through a verythin film (thickness d) of titania (TiO₂, n₁=2.35) into silica again. Itcan be seen that when d/λ_(eff) is less than 0.1, more than 90% of thelight will be transmitted. Hence, a general guideline is that when thethickness of the thin film is less than about

$\frac{\lambda}{10n_{2}\cos \; \theta},$

more than 90% of the light will pass through the film. If the light beamshines onto the film at normal incidence (i.e. θ=θ°), the single layerfilm thickness is advantageously chosen to be less than

$\frac{\lambda}{10n_{2}},$

which is about 66 nm for TiO₂ and about 100 nm for SiO₂. In GRIN-lensfocusing applications, the light wave travels paraxially along thecentral axis, so that the angle θ varies from 90° to about 60°.Accordingly, the fraction of light transmitted is generally more than95% if single layer thicknesses less than

$\frac{\lambda}{10n_{2}}$

are used.

To evaluate the focusing power of the GRIN device, light wavepropagation was simulated for a first GRIN lens having a parabolicrefractive index distribution made up of thin layers of numerousdifferent materials, substantially approximating a continuous indexdistribution, and for a second GRIN lens made up of layers of only twomaterials. FIGS. 4A-B show the simulation result for a parabolicrefractive index distribution of

${{n(r)} = {n_{0}\left\lbrack {1 - {\Delta \left( \frac{r}{a} \right)}^{2}} \right\rbrack}},$

with a=5 μm, n₀=1.75 and n_(b)=1.45. FIG. 4A shows results for the asubstantially continuous GRIN lens, and FIG. 4B shows results for thetwo material GRIN lens. As can be seen, both GRIN lenses have similarfocal lengths and focused spot sizes.

To evaluate the energy loss for light propagating longitudinally throughthe device, the optical energy flow was calculated based on integrationover space of the standard electromagnetic energy flow vector {rightarrow over (S)}={right arrow over (E)}×{right arrow over (H)}, where{right arrow over (E)}×{right arrow over (H)} are the electric andmagnetic fields. FIGS. 5A-B show simulation results for a two materialGRIN lens and a many material GRIN lens, respectively. In bothsimulations, it has been assumed that there is no material absorption oflight and all the interfaces are perfect. Each GRIN lens extends frompoint A to point D, so that the focal point is just outside the GRINlens. A semiconductor waveguide made of Indium phosphide (InP), with itsmode matched to the focused beam profile, extends from point B to pointC, leaving an air gap of 1 μm between the GRIN lens and thesemiconductor waveguide. Antireflection coatings have been included onboth the GRIN lens end face and on the InP waveguide end face. Table 1shows light energy transmission efficiency for each GRIN lens. The twomaterial case is not significantly different from the substantiallycontinuous case.

TABLE 1 Two-material Substantially case Continuous case Fraction oflight energy passed 99.9% 98.8% through the GRIN lens from A to BFraction of light energy passed from 99.7% 99.5% B to C (including modematching) Fraction of light energy within the 95.6% 98.2% InP waveguideat C (i.e., within 3× width of the waveguide) Overall couplingefficiency 95.3% 97.7%

The foregoing analyses indicate that a GRIN device made up ofalternating layers of two different materials can provide hightransmission efficiency, a short focal length, a small focused spotsize, and acceptably low energy loss when coupling to a small mode sizewaveguide or other optical components.

Fabrication of such a structure is straightforward; existingtechnologies for fabricating thin film dense wavelength divisionmultiplexing (DWDM) filters for optical communications by depositingsuccessive layers of materials can be adapted to fabricating GRINdevices. Deposition methods that may be employed to create the structureinclude sputtering, chemical vapor deposition, electron beam and thermalevaporation, ion beam deposition or dual ion beam deposition (alsocalled ion assisted deposition, or IAD), sol gel spin or dip coating andothers.

One embodiment of the present invention consists of a large number(e.g., 306) of alternating thin layers of silica (SiO₂) and titania(TiO₂) on a flat silicon substrate. The thickness of each layer (in nm)for this embodiment is listed in Table 2. A thicker buffer layer of SiO₂(1 μm) is deposited first in order to separate the GRIN device from thesubstrate material so that light will not leak into the substrate. Asidefrom the buffer layer, the thicknesses of the silica layers range from20 nm to 70 nm, and the thicknesses of the titania layers range from 20nm to 80 nm. In regions where the effective index of refraction is high,titanic layers are near their thickest while silica layers are neartheir thinnest; in regions where the effective index is low, the reverseapplies.

FIG. 6 shows an scanning electron microscope (SEM) image of such astructure deposited on a flat Si substrate, and FIG. 7A shows themeasurement result of such a structure acting as a one dimensional GRINlens to focus a light beam from a standard single mode fiber into anelliptical beam; as a comparison the output beam profile from a standardsingle mode fiber is shown in FIG. 7B.

It should be noted that a planar layered structure would focus lightonly in the direction transverse to the plane of the layers (thevertical direction for horizontal layers on a substrate). In the lateralor horizontal direction, light beam size transformation can be achievedusing tapered waveguide structures, e.g., as described in the abovereferenced copending U.S. patent application Ser. No. 10/083,674.

TABLE 2 Mtl nm TiO2 60 SiO2 20 TiO2 50 SiO2 20 TiO2 60 SiO2 20 TiO2 50SiO2 20 TiO2 60 SiO2 20 TiO2 50 SiO2 20 TiO2 60 SiO2 20 TiO2 50 SiO2 20TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 50 SiO2 20TiO2 80 SiO2 30 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20TiO2 50 SiO2 20 TiO2 70 SiO2 30 TiO2 S0 SiO2 20 TiO2 70 SiO2 30 TiO2 70SiO2 30 TiO2 70 SiO2 30 TiO2 S0 SiO2 20 TiO2 40 SiO2 20 TiO2 S0 SiO2 20TiO2 40 SiO2 20 TiO2 70 SiO2 30 TiO2 40 SiO2 20 TiO2 70 SiO2 30 TiO2 40SiO2 20 TiO2 70 SiO2 30 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 S0 SiO2 30TiO2 40 SiO2 20 TiO2 50 SiO2 30 TiO2 40 SiO2 20 TiO2 S0 SiO2 30 TiO2 40SiO2 20 TiO2 30 SiO2 20 TiO2 40 SiO2 20 TiO2 30 SiO2 20 TiO2 40 SiO2 20TiO2 40 SiO2 30 TiO2 40 SiO2 20 TiO2 40 SiO2 30 TiO2 40 SiO2 20 TiO2 40SiO2 30 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30SiO2 20 TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 40 SiO2 30TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 20 SiO2 20 TiO2 40SiO2 30 TiO2 20 SiO2 20 TiO2 40 SiO2 30 TiO2 20 SiO2 20 TiO2 40 SiO2 30TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 40 SiO2 30 TiO2 20 SiO2 20 TiO2 20SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20TiO2 20 SiO2 20 TiO2 20 SiO2 40 TiO2 30 SiO2 20 TiO2 20 SiO2 20 TiO2 20SiO2 40 TiO2 30 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 40 TiO2 30 SiO2 20TiO2 30 SiO2 40 TiO2 30 SiO2 40 TiO2 30 SiO2 40 TiO2 30 SiO2 40 TiO2 30SiO2 40 TiO2 30 SiO2 40 TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 20 SiO2 30TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 30SiO2 S0 TiO2 20 SiO2 40 TiO2 30 SiO2 S0 TiO2 20 SiO2 40 TiO2 30 SiO2 S0TiO2 20 SiO2 40 TiO2 20 SiO2 40 TiO2 20 SiO2 40 TiO2 20 SiO2 40 TiO2 20SiO2 40 TiO2 20 SiO2 S0 TiO2 20 SiO2 40 TiO2 20 SiO2 50 TiO2 20 SiO2 50TiO2 20 SiO2 50 TiO2 20 SiO2 S0 TiO2 20 SiO2 S0 TiO2 20 SiO2 60 TiO2 20SiO2 60 TiO2 20 SiO2 60 TiO2 20 SiO2 70 TiO2 20 SiO2 70 TiO2 20 SiO2 70TiO2 20 SiO2 20 SiO2 1000

In an alternative embodiment, multiple thin layers may be deposited on anon planar substrate surface. There are various ways to reshape a flatsubstrate surface into other kinds of surface profiles. For example,known micro machining techniques can be used to create a curved surface.Gray scale masks can also be used to create a surface relief pattern ona photoresist film, and such a pattern can be transferred downward toanother material below the photoresist film. As is illustrated in FIG.8, a U-shaped groove 801 can be created in a substrate 802, and amultilayer film 804 made of alternating layers of two materials can bedeposited in the U groove (FIG. 8A). A planarization processing step canbe used to create the bottom half 805 of a two-dimensional GRIN lens(FIG. 8B). A gray scale mask can be used to make a convex surfaceprofile 806 on the existing half-GRIN structure 805 (FIG. 8C), and morelayers 807 can be deposited on top of the convex surface to make atwo-dimensional GRIN lens 808 (FIG. 8D) for light focusing applicationsin which focusing light in both the horizontal and vertical directionsis desired. Gray scale mask techniques are used in microlens fabricationand are described in the above referenced co-pending U.S. patentapplication Ser. No. 10/083,674.

It should be noted that structures other than alternating layers of twomaterials could be used. For instance, a third material (or more) couldbe added in some alternative embodiments. In another alternativeembodiment, small size grains or dots of one material are embedded inanother material with the grains or dots having different density and/orgrain size distributions in different parts of the material. Also, wiresof one material can be embedded into another material, with the wireshaving a desired distribution of density or size. In addition, acombination of embedded grains and wires could be used, and this couldbe further combined with thin layers. Thus, any mixture of small sizestructures may be used to create graded refractive index devicessuitable for various applications.

A variety of materials can also be used, including amorphous andpolycrystalline materials. For example, silica (SiO₂ n=1.45) and titania(TiO₂, n=2.35) are in common use for making thin film filters foroptical fiber communication applications. Due to their relatively largerefractive index difference (about 0.9), they can be used to createeffective graded refractive index devices for many light focusingapplications. A number of other materials may also be used, such astantalum pentoxide (Ta₂O₅), zirconium oxide (ZrO₂), niobium pentoxide(Nb₂O₅), hafnium oxide (HfO₂), zinc oxide (ZnO), germanium oxide (GeO₂),lead oxide (PbO), yttrium oxide (Y₂O₃), aluminum oxide (Al₂O₃), siliconcarbide (SiC), titanium carbide (TiC), titanium nitride (TiN), chromiumnitride (CrN), carbon nitride (CN), carbon boride (CB), aluminum nitride(AlN), zinc selenide (ZnSe), barium fluoride (BaF₂), magnesium fluoride(MgF₂), diamond like carbon (DLC), silicon (Si), germanium (Ge),polyimide, bisbenzocyclobutene (BCB) and cyclized transparent opticalpolymer (CYTOP). It should be noted that the refractive index of some ofthese materials is quite large (e.g., for silicon, n=3.4). The choice ofmaterials can be varied, depending on the particular application.

One advantageous choice of materials is silicon (Si) and silica (SiO₂).When Si is combined with SiO₂, the effective refractive index of theresulting medium can vary by as much as about 1.9. This large variation,combined with the high refractive index of silicon, may be useful insome applications because of the short focal length and small spot size(0.4 μm in one simulation) that can be achieved.

GRIN devices according to embodiments of the present invention may beused in any application where there is a need to focus a light beam intoa small spot size. For example, such couplers can be used to focus lightfrom a single mode optical fiber into a III-V semiconductor waveguide,in place of objective lenses or lens tipped fibers. Through properselection of the refractive index distribution, mode matching to thefiber and the semiconductor waveguide can be achieved. Such devices canbe fabricated on a substrate as part of an integrated coupler structurethat includes a U-groove or V-groove for holding an optical fiber and aphotonic chip mounting recess for holding the semiconductor waveguide.Some examples of such optical coupling systems are described in detailin the above referenced co pending U.S. patent application Ser. No.______ (Attorney Docket No. 10095/19). Still further examples aredescribed in detail in the above referenced co pending U.S. patentapplication Ser. No. 10/083,674.

In addition to light beam focusing, GRIN devices according toembodiments of the present invention can also be used in otherapplications. For instance, in many near field optics applications,transformation of alight beam from a mode profile corresponding to astandard single mode optical fiber to a smaller mode size is generallyachieved by tapering the fiber to a small tip (e.g., tens of nanometers)at one end and coating the outside of the tapered region with a metalfilm to prevent light from escaping. In general, most of the light (asmuch as 99.99%) is lost during this beam size transformation process.Replacing such tapered fibers with GRIN devices according to embodimentsof the present invention can improve the transmission efficiencysubstantially.

Another application relates to optical data storage, where the storagedensity can be limited by the spot size of light beams used to recordand/or read the data. In existing optical storage devices, discreteoptical elements (prisms, lenses, wave plates, etc.) are used to makethe optical head and to focus a light beam from a semiconductor laser toa spot size of a few microns. Using a GRIN device according to anembodiment of the present invention, the focused spot size can be mademuch smaller, and the storage density can be substantially increased. Inaddition, discrete optical elements can also be replaced with planarlight wavecircuit based integrated optics.

It will also be appreciated that GRIN devices according to embodimentsof the present invention allow for fine control and tuning of therefractive index and refractive index distribution to achieve a precise,arbitrary refractive index profile, thereby allowing precise shaping ofthe optical spot size and mode (wavefront) profile of transmitted light.Thus, such multilayer devices are also suitable for use in a variety ofoptical applications, including applications where the difference inrefractive index is small (e.g., less than 0.2).

The physical size of the GRIN device can also be varied. For example, atwo material device could be constructed for coupling light between asemiconductor laser or detector and a standard multimode fiber, whichtypically has a mode size of about 50 to 65 microns. It can also be usedto couple light from a one dimensional or two dimensional semiconductorlaser array or laser bar into a single mode fiber, e.g., for opticallypumping an erbium doped fiber amplifier.

It should be understood that various alternatives to the embodiments ofthe invention described herein may be employed in practicing theinvention. It is intended that the following claims define the scope ofthe invention and that methods and structures within the scope of theseclaims and their equivalents be covered thereby.

1. An optical module comprising: a substrate assembly including aphotonic chip mounting region and a groove extending toward the photonicchip mounting region; and an optical coupler having a graded index ofrefraction disposed between the groove and the photonic chip mountingregion, the optical coupler including: a plurality of alternating layersof a first material and a second material, each layer of the secondmaterial having a thickness substantially less than an effectivewavelength of light in the second material, wherein at least one of thefirst and second materials is an amorphous material, the first materialhaving a first index of refraction, the second material having a secondindex of refraction different from the first index of refraction, theplurality of alternating layers forming a light transmitting medium withan effective index of refraction in a local region that depends on alocal ratio of a volume of the layers of the first material to a volumeof the layers of the second material, wherein a graded effective indexof refraction along a direction transverse to the layers is formed byvarying the thicknesses of the layers.
 2. The optical system of claim 1,wherein the optical coupler further includes: a buffer layer comprisingone of the first and second amorphous materials disposed between thesubstrate and a lowest one of the plurality of alternating layers. 3.The optical system of claim 1, wherein the effective index of refractionvaries such that a mode profile of light propagating through the opticalcoupler is transformed from a first mode profile substantially matchinga mode profile for light propagating in a single mode fiber to a secondmode profile substantially matching a mode profile for light propagatingin a semiconductor waveguide.
 4. The optical system of claim 1, whereinthe second index of refraction is different from the first index ofrefraction by at least 0.2.
 5. The optical system of claim 1, whereinthe first material comprises silicon dioxide and the second materialcomprises titanium dioxide.
 6. The optical system of claim 1, whereinthe first material comprises silicon dioxide and the second materialcomprises tantalum pentoxide.
 7. The optical system of claim 1, whereinthe first material comprises silicon dioxide and the second materialcomprises silicon.
 8. The optical system of claim 1, wherein the grooveis a V groove or a U-groove.
 9. The optical system of claim 1, furthercomprising: a photonic chip mounted in the photonic chip mountingregion.
 10. The optical system of claim 1, further comprising: anoptical fiber mounted in the groove.